Yair Lapid has emerged as the most serious political rival to Netanyahu

TEL AVIV—The man predicted to win Israeli elections if they were held today picks a seemingly contradictory way of describing himself: “an extreme moderate.”

Once dismissed as a passing fad, Yair Lapid, a 53-year-old former TV anchor, has emerged as the most serious political rival to Prime Minister Benjamin Netanyahu. And he has done so by trying to dispense with the traditional left-right divide of Israeli politics, adopting...